Invariant Dirac Operators, Harmonic Spinors, and Vanishing Theorems in CR Geometry

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2021
• Main Author: Leitner, Felipe
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2021
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211177
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Invariant Dirac Operators, Harmonic Spinors, and Vanishing Theorems in CR Geometry. Felipe Leitner. SIGMA 17 (2021), 011, 25 pages

We study Kohn-Dirac operators θ on strictly pseudoconvex CR manifolds with spinℂ structure of weight ℓ ∈ ℤ. Certain components of θ are CR invariants. We also derive CR invariant twistor operators of weight ℓ. Harmonic spinors correspond to cohomology classes of some twisted Kohn-Rossi complex. Appl...